There are 12 members in a group. In how many | vedclass

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Question

(B) We need to select $6$ members from a total of $12$ members.Since one particular member must always be included,we have already selected $1$ member

Vedclass · Accepted Answer

$462$

Vedclass · Answer

(B) We need to select $6$ members from a total of $12$ members.Since one particular member must always be included,we have already selected $1$ member.Now,we need to select the remaining $6 - 1 = 5$ members from the remaining $12 - 1 = 11$ members.The number of ways to select $5$ members from $11$ is given by the combination formula ${}^{n}C_{r} = \frac{n!}{r!(n-r)!}$.Therefore,the number of ways is ${}^{11}C_{5} = \frac{11 	imes 10 	imes 9 	imes 8 	imes 7}{5 	imes 4 	imes 3 	imes 2 	imes 1} = 11 	imes 3 	imes 2 	imes 7 = 462$.

There are $12$ members in a group. In how many ways can a team of $6$ members be selected such that a particular member is always included?

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